Parabola of 4th and 5th Intervals

In an earlier lesson we learned that one octave has 12 sounds and 21 letters to "spell" 15 major scales in 15 major keys. Now, in this lesson, we will see how those 15 major keys connect in a “broken circle” of 4th and 5th intervals.
Simply stated, up a perfect fourth arrives at the same "key letter" as down a perfect fifth, but sounds one octave higher in pitch. The opposite is also true, down a perfect fourth arrives at the same key letter as up a perfect fifth, but sounds one octave lower. I call this the "law of nine" because "rules", like circles, can be broken!
What becomes apparent as we look at this "new view" of what is incorrectly called the "circle" of 4ths and 5ths - is that it’s not a circle at all - but rather, more like a parabola, which can be thought of as two curved lines that start in one place (C major), but end at two different places (C♭ major and C♯ major).
The point of this lesson is to show that the only way to start at "C" and continue in the same "circular" direction to get back to "C", is to modulate (change keys) at one of the enharmonic keys: D♭/C♯, G♭/F♯ or C♭/B. This will become more meaningful as we begin to explore harmony progressions in later lessons.

Till next time, have some parabolic fun, no matter what key you’re in or direction you’re headed. I’m listening and I’m here for you...